Brown 1 lb Italian sausage in a large saucepan over med-high heat. Add onion and carrot ;saute 3 minutes.
Stir in garlic. Saute another 3 minutes.
Add broth and tomatoes; bring to boil. Stir in Pasta and simmer until cooked, about 10 minutes.
Add spinach and pesto and cook about 1 minute more to wilt spinach and distribute pesto.